Add full Postgres support and migrate from SQLite

[bogdanserdinov]

Currently, the application primarily relies on SQLite, with only partial support for Postgres in some queries. To improve scalability, reliability, and production readiness, we want to introduce full Postgres support and migrate the application to use Postgres as the primary database.
This change must be implemented in a way that preserves all existing functionality and ensures backward compatibility with the current SQLite schema.

The goal is to:

1. Fully support PostgreSQL across the entire application
2. Ensure schema compatibility with the existing SQLite structure
3. Maintain identical behavior and functionality after migration
4. Provide an easy setup for developers using Docker